Perturbation Analysis for t-Product-Based Tensor Inverse, Moore-Penrose Inverse and Tensor System

doi:10.1007/s42967-022-00186-1

Communications on Applied Mathematics and Computation ›› 2022, Vol. 4 ›› Issue (4): 1441-1456.doi: 10.1007/s42967-022-00186-1

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Perturbation Analysis for t-Product-Based Tensor Inverse, Moore-Penrose Inverse and Tensor System

Zhengbang Cao, Pengpeng Xie

School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, Shandong, China

收稿日期:2021-08-30 修回日期:2022-01-21 出版日期:2022-12-20 发布日期:2022-09-26
通讯作者: Pengpeng Xie,E-mail:xie@ouc.edu.cn;Zhengbang Cao,E-mail:caozhengbang@stu.ouc.edu.cn E-mail:xie@ouc.edu.cn;caozhengbang@stu.ouc.edu.cn
基金资助:
The authors would like to thank two anonymous referees for their useful comments which led to significant improvements. We also deeply appreciate feedback on an earlier version of this manuscript from Professor Eric King-Wah Chu. This work is supported by the National Natural Science Foundation of China under grant number 11801534.

Perturbation Analysis for t-Product-Based Tensor Inverse, Moore-Penrose Inverse and Tensor System

Zhengbang Cao, Pengpeng Xie

School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, Shandong, China

Received:2021-08-30 Revised:2022-01-21 Online:2022-12-20 Published:2022-09-26
Supported by:
The authors would like to thank two anonymous referees for their useful comments which led to significant improvements. We also deeply appreciate feedback on an earlier version of this manuscript from Professor Eric King-Wah Chu. This work is supported by the National Natural Science Foundation of China under grant number 11801534.

摘要/Abstract

摘要： This paper establishes some perturbation analysis for the tensor inverse, the tensor Moore-Penrose inverse, and the tensor system based on the t-product. In the settings of structured perturbations, we generalize the Sherman-Morrison-Woodbury (SMW) formula to the t-product tensor scenarios. The SMW formula can be used to perform the sensitivity analysis for a multilinear system of equations.

关键词: Perturbation analysis, Moore-Penrose inverse, tensor inverse, Multilinear system, Sherman-Morrison-Woodbury (SMW) formula

Abstract: This paper establishes some perturbation analysis for the tensor inverse, the tensor Moore-Penrose inverse, and the tensor system based on the t-product. In the settings of structured perturbations, we generalize the Sherman-Morrison-Woodbury (SMW) formula to the t-product tensor scenarios. The SMW formula can be used to perform the sensitivity analysis for a multilinear system of equations.

Key words: Perturbation analysis, Moore-Penrose inverse, tensor inverse, Multilinear system, Sherman-Morrison-Woodbury (SMW) formula

中图分类号:

65F05
15A69

Zhengbang Cao, Pengpeng Xie. Perturbation Analysis for t-Product-Based Tensor Inverse, Moore-Penrose Inverse and Tensor System[J]. Communications on Applied Mathematics and Computation, 2022, 4(4): 1441-1456.

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Perturbation Analysis for t-Product-Based Tensor Inverse, Moore-Penrose Inverse and Tensor System

Perturbation Analysis for t-Product-Based Tensor Inverse, Moore-Penrose Inverse and Tensor System

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